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  • 1
    Electronic Resource
    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 56 (2000), S. 340-347 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: In general, the local atomic environment becomes less symmetric owing to point defects and thermal vibrations of atoms in crystals. It is shown that, as a result of this phenomenon, an additional anisotropy of the resonant scattering factors can occur and the forbidden Bragg reflections can be excited near absorption edges. Examples of crystals are presented (Ge, K2CrO4, C-15 type) where such thermal-motion-induced (TMI) and point-defect-induced (PDI) reflections can be observed. The tensor structure factors of both types of reflection are computed. Owing to their resonant character, the PDI reflections allow both impurity atoms and host atoms of different types to be studied separately. The considered phenomena can provide a very sensitive method to study point defects because only the atoms distorted by defects produce contributions to the PDI reflections.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 53 (1997), S. 388-395 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The X-ray extinction conditions are studied for the cases when both magnetic interaction and crystalline fields cause the anisotropy of X-ray scattering amplitudes near the absorption edge. It is demonstrated that the simultaneous existence of those two anisotropies, referred to as the combined anisotropy, can result in excitation of additional Bragg reflections otherwise forbidden by extinction rules. To show this, the structure amplitudes of reflections are computed and two Laue (L) groups are compared: one, Lm, which corresponds to the anomalous X-ray scattering in the presence of magnetic structure and another one, Lq, which takes into account the anisotropic atomic environment. Both groups can contain additional reflections and differ from the Laue group, Lp, associated with the usual potential X-ray scattering. The cross of these groups is considered and it is shown that several extinctions, typical for the Lp group, still remain in Lq and Lm. Nevertheless, the new reflections may appear instead of those extinctions when the combined anisotropy is taken into account. In this case, the diffraction pattern is characterized by the Lc group. Then, the transformation of Lq into Lc under the phase transition is studied. It is shown that the additional reflections, not typical for Lm, can appear in the diffraction pattern below the magnetic ordering temperature TM. Two cases are discussed: (i) Lq above TM contains the same reflections as Lc and (ii) Lq contains the extinctions corresponding to the additional reflections in Lc. Several examples are considered for real magnetic crystals.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 56 (2000), S. 2-10 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: The general form of the X-ray susceptibility tensor near absorption edges is found when several anisotropic factors, such as the anisotropy of local atomic environment, magnetic ordering and orbital ordering, simultaneously exist in a crystal. Different phenomenological approaches are used to obtain the explicit form of the susceptibility tensor and to find the contributions from each anisotropic factor separately as well as `combined' terms owing to their simultaneous existence. The results of the theoretical treatment are applied to the resonant diffraction by La0.5Sr1.5MnO4 below the Néel temperature, where charge and orbital ordering coexist with anisotropy of local atomic environment and magnetic ordering.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 57 (2001), S. 642-648 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: It is shown that additional Bragg reflections can appear exclusively owing to the local chirality associated with the left–right asymmetric environment of scattering atoms in non-magnetic crystals. The structure amplitude of these reflections depends on the antisymmetric part of a third-rank tensor describing the spatial dispersion effects. It enhances for resonant near-edge scattering through a mixed multipole transition, which includes a dipole–quadrupole contribution. It is shown that this mechanism works even for centrosymmetric crystals, and some realistic examples are considered in detail (α-Fe2O3, LiNbO3 etc.). For instance, the interference between the dipole–quadrupole and quadrupole–quadrupole terms may be responsible for the threefold symmetry of the azimuthal dependence of the hhh, h = 2n + 1, reflections observed recently in hematite.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    [S.l.] : International Union of Crystallography (IUCr)
    Acta crystallographica 55 (1999), S. 20-29 
    ISSN: 1600-5724
    Source: Crystallography Journals Online : IUCR Backfile Archive 1948-2001
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Symmetry restrictions on the intensities and polarization properties of main reflections and their satellites are found for incommensurately modulated crystals in the case of anisotropic anomalous X-ray diffraction near absorption edges. It is shown that the modulation becomes a source of additional anisotropy for each resonant scatterer and induces a modulated behaviour of the susceptibility tensor. The four-dimensional approach is used to calculate the set of possible reflections. It is found that additional (`forbidden') reflections may appear both in the system of main reflections and in the system of satellites. The anisotropy also results in complex azimuthal and polarization properties of each reflection. The displacive modulation is discussed in detail. The ATS reflections corresponding to the resonant X-ray diffraction near the K-edge of iron in pyrrhotite-5.5C are considered.
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Springer
    JETP letters 69 (1999), S. 938-942 
    ISSN: 1090-6487
    Keywords: 78.70.Ck ; 61.10.Eq
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A new type of x-ray spectroscopy is proposed which can detect the thermal-motion-induced distortions of atomic electronic states in crystals. It is shown that those distortions can cause extra Bragg reflections (so-called forbidden reflections) and that their intensity should grow with increasing temperature. The reason is that the thermal displacements, which change the symmetry of atomic environment, can modify the tensor amplitude of x-ray resonant scattering. In the first approximation, the structure factor of extra reflections is proportional to the reflection vector H and to the mean-square thermal displacement $$\overline {u_j u_k } $$ for optical phonons. It is demonstrated that the forbidden resonant reflections, observed recently in Ge, could be caused by the thermal motion.
    Type of Medium: Electronic Resource
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